Theorem 7 
For contextual linear bandits with unknown corruption that is bounded by \(C\) , Algorithm REF  with \(t^{(m)}=2^{m-1}\)  and \(\Lambda _{\epsilon _m}\)  being G-COBE in [1]} with PE, that uses \(\gamma _m\)  in (REF ), as a subroutine, achieves
\(R_T=\tilde{O}(d\sqrt{T}+d^{1.5}C)\) 
